Write the quadratic function f(x) = 3x² - 6x + 9 in vertex form.

Solution:

Vertex form of a quadratic equation refers to (x - h)² = 4a (y - k) form or (y - k)² = 4a (x - h) form depending on whether the square is on x-term or y-term respectively.

Given quadratic function is f(x) = y = 3x² - 6x + 9

In the given equation square term is for x.

∴ Equation must be reduced to (x - h)² = 4a (y - k) form.

We have y = 3x² - 6x + 9

⇒ y = 3 (x² - 2x + 3)

⇒ y = 3 (x² - 2x + 1 + 2)

⇒ y = 3 [(x - 1)² + 2]

⇒ y = 3(x - 1)² + 6

⇒ y - 6 = 3(x - 1)²

⇒ 3(x - 1)² = y - 6

The above equation is in the vertex form.

Write the quadratic function f(x) = 3x² - 6x + 9 in vertex form.

Summary:

The vertex form of the given quadratic function, f(x) = 3x² - 6x + 9, is 3(x - 1)² = y - 6.